The other thing that is overlooked in the RNG debate is the difference between evaluating the RNG for all pulls across the game vs the RNG for individuals.
It may be quite easy for Kabam to do a data dump and say that of the million 5* crystals opened there was a literal even chance for any champ in the crystal. However, that pure RNG is the balance of some players who are skewed one way and other players skewed differently.
Player A may have a higher chance for champs 1-3, whereas Player B has a higher chance for 4-6. When you evaluate all pulls, then the cumulative RNG says there was an even chance for all 6.
The problem is there is really no true evidence Kabam could really publish that would really confirm or deny whether RNG is equally weighted or not unless some programmer analyzed their system and was able to say with 100% conviction that everything is equal.
It is almost impossible to prove the negative: that of all possible ways to tamper with or skew the random rewards exactly none of them exist in the system. And I would never make that claim. It is possible to constrain what kind of tampering could be happening. People used to talk about PHCs being weighted. I did the actual analysis of this back in the day, and I could state with reasonable certainty that PHCs were not being weighted at the time to within about one part in a thousand. Since no one was claiming that Kabam had their fingers on the scales to that tiny amount, that analysis conclusively disproved all of the manipulation accusations that were running around at the time. Incidentally, that analysis of PHCs also ended up agreeing with the eventually published odds of PHC crystals, except it predicted about half the rate of 4* champs, and when the odds were published people noticed a dramatic uptick in the rate of getting 4* champs which suggested my numbers were different because Kabam changed the crystal. Besides that, I was more or less on the money. So that suggests the analysis was probably correct and probably contained enough data to make reasonable conclusions.
I also did two meta-analyses of other statistical data gathering looking for statistical variance in things like 4* crystals, 5* crystals, and (F)GMCs. In all cases I could not find one to within about two percentage points. And keep in mind it was my 5* featured analysis back in the day that first constrained the featured crystal to a 15%-25% chance for featured, that eventually narrowed down to about 20% plus or minus a couple percent.
I've also looked at crystal openings that compare paid vs free to play accounts, and openings verses future openings (i.e. does one opening affect the next one). Out of all of those analyses, only one showed a statistically significant signal, but at a very low confidence level. Back in the day there was a very tiny increase in the number of duplicate champs pulled from sets of crystals relative to the predicted chance. Enough to make me raise an eyebrow, but not enough to be remotely conclusive.
I can't say the random rewards are perfectly random. I don't have enough data to say that. I can say that I haven't heard a theory about a *specific* kind of non-randomness that the data isn't large enough to disprove. Until someone proposes a theory about how the crystals are non-random that a) is a kind of variation that a human actually could detect through observation in theory, b) makes testable predictions, and c) has those predictions confirmed, my skepticism saying don't trust what Kabam says, don't trust player gut instincts, trust the data. The data says the crystal drops are sufficiently random to beat all randomness tests I can think of performing (and have the time to perform). That's an objective statement about the crystals that requires trusting no one.
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It may be quite easy for Kabam to do a data dump and say that of the million 5* crystals opened there was a literal even chance for any champ in the crystal. However, that pure RNG is the balance of some players who are skewed one way and other players skewed differently.
Player A may have a higher chance for champs 1-3, whereas Player B has a higher chance for 4-6. When you evaluate all pulls, then the cumulative RNG says there was an even chance for all 6.
It is almost impossible to prove the negative: that of all possible ways to tamper with or skew the random rewards exactly none of them exist in the system. And I would never make that claim. It is possible to constrain what kind of tampering could be happening. People used to talk about PHCs being weighted. I did the actual analysis of this back in the day, and I could state with reasonable certainty that PHCs were not being weighted at the time to within about one part in a thousand. Since no one was claiming that Kabam had their fingers on the scales to that tiny amount, that analysis conclusively disproved all of the manipulation accusations that were running around at the time. Incidentally, that analysis of PHCs also ended up agreeing with the eventually published odds of PHC crystals, except it predicted about half the rate of 4* champs, and when the odds were published people noticed a dramatic uptick in the rate of getting 4* champs which suggested my numbers were different because Kabam changed the crystal. Besides that, I was more or less on the money. So that suggests the analysis was probably correct and probably contained enough data to make reasonable conclusions.
I also did two meta-analyses of other statistical data gathering looking for statistical variance in things like 4* crystals, 5* crystals, and (F)GMCs. In all cases I could not find one to within about two percentage points. And keep in mind it was my 5* featured analysis back in the day that first constrained the featured crystal to a 15%-25% chance for featured, that eventually narrowed down to about 20% plus or minus a couple percent.
I've also looked at crystal openings that compare paid vs free to play accounts, and openings verses future openings (i.e. does one opening affect the next one). Out of all of those analyses, only one showed a statistically significant signal, but at a very low confidence level. Back in the day there was a very tiny increase in the number of duplicate champs pulled from sets of crystals relative to the predicted chance. Enough to make me raise an eyebrow, but not enough to be remotely conclusive.
I can't say the random rewards are perfectly random. I don't have enough data to say that. I can say that I haven't heard a theory about a *specific* kind of non-randomness that the data isn't large enough to disprove. Until someone proposes a theory about how the crystals are non-random that a) is a kind of variation that a human actually could detect through observation in theory, b) makes testable predictions, and c) has those predictions confirmed, my skepticism saying don't trust what Kabam says, don't trust player gut instincts, trust the data. The data says the crystal drops are sufficiently random to beat all randomness tests I can think of performing (and have the time to perform). That's an objective statement about the crystals that requires trusting no one.